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is larger than 0.5. The bottom flow B does not have a direct impact on the bottom quality; it could have some impact via a level controller.

For top quality, R, W and S are all suitable candidates for control. If, however, pressure is controlled by manipulating coolant W, the only viable option for bottom composition control is the steam flow S, after which the only remaining option for control of the top quality is the reflux R. Not in all cases, however, is there a dual composition requirement, which leaves more options for composition control.

It is important to provide the column with adequate sensors: flow measurements and pressure measurements at various locations, for example above the top tray, at the feed tray and below the bottom tray in order to be able to calculate pressure differentials for the purpose of detecting flooding. Temperature sensors should also be positioned at various locations along the column. In many cases temperatures can be used to infer composition. When the temperature difference between top and bottom of the column is small, inferring composition from temperature measurements is generally not feasible, even though in some cases temperature differences may still provide a reasonable composition estimate. An advantage of using temperature differences is that it is insensitive to pressure changes; unfortunately, the correlation between temperature difference and product composition is often highly nonlinear. In multicom-ponent mixtures, the relation of tray temperature to key component composition is not unique. Furthermore, the tray temperature to key product composition may also be nonlinear. Therefore, care must be taken in using temperatures for controlling composition. For high purity distillation columns sometimes the logarithm of the temperature (or composition) is used to linearize the response of the distillation column.

When the temperature difference between column top and bottom is large, several temperatures should be measured at trays above and below the feed tray, where under normal circumstances the temperature break is located. These temperatures should then be averaged and could be used in manipulating, for example, the steam flow.

An excellent treatment of sensor and valve issues in distillation control is given by Luyben (see Further Reading); the location of temperature sensors receives an especially comprehensive treatment.

For a distillation column first the base control scheme should be established, i.e. pressure, reflux drum level and column bottoms level should be controlled. Then two variables remain available for control of composition, say the reflux R and steam flow S.

If temperature is used for control of composition, the problem of proper temperature sensor location becomes prime importance.

If only one composition is controlled, a simple procedure could be followed. By giving a small change in the reflux R, the sensitivity ÔT-JÔR can be determined for each tray. A similar procedure can be followed for the steam flow S. A typical plot for a toluene-o-xylene column with 30 trays is shown in Figure 7. It can be seen that a 1% change in steam

Reflux 1

Figure 7 Gain matrix graph for the toluene-o-xylene column.

Reflux 1

Figure 7 Gain matrix graph for the toluene-o-xylene column.

flow causes a temperature change of about 10° at tray 24. A 1% change in the reflux flow causes a maximum temperature change on tray 26 of about — 4°. Therefore the sensitivity of the temperature to changes in steam flow is larger than the sensitivity for changes in reflux flow. Where there is dual composition control, sensor sensitivity should be balanced against sensor interaction. One tool that has been used to accomplish this is singular value decomposition. The sensitivity matrix X, which contains the sensitivity of the temperature on each tray for changes in reflux and steam and thus contains two columns and 30 rows, is now decomposed into three individual matrices:

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